\thispagestyle {empty}
\contentsline {chapter}{\numberline {1}Introduction}{1}{chapter.1}
\contentsline {chapter}{\numberline {2}Background}{3}{chapter.2}
\contentsline {section}{\numberline {2.1}History}{3}{section.2.1}
\contentsline {section}{\numberline {2.2}What Is A Cellular Automaton}{4}{section.2.2}
\contentsline {section}{\numberline {2.3}How Cellular Automata Work}{5}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}Ecological Simulation}{5}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}Discrete Step Rules}{6}{subsection.2.3.2}
\contentsline {subsection}{\numberline {2.3.3}Less Common Rules}{9}{subsection.2.3.3}
\contentsline {subsection}{\numberline {2.3.4}Movement}{9}{subsection.2.3.4}
\contentsline {subsection}{\numberline {2.3.5}Continuous Time}{10}{subsection.2.3.5}
\contentsline {chapter}{\numberline {3}Simulator}{12}{chapter.3}
\contentsline {section}{\numberline {3.1}Using the simulator}{12}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}Rules}{13}{subsection.3.1.1}
\contentsline {section}{\numberline {3.2}Implementation}{13}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}Cellular Automata}{14}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}Gillespie Simulator}{15}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}Spatial Indices}{16}{subsection.3.2.3}
\contentsline {section}{\numberline {3.3}GUI}{19}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}Grid}{19}{subsection.3.3.1}
\contentsline {subsection}{\numberline {3.3.2}Chart}{20}{subsection.3.3.2}
\contentsline {chapter}{\numberline {4}Experiments}{21}{chapter.4}
\contentsline {section}{\numberline {4.1}Replication of Ruxton and Saravia with added Gillespie Simulator}{21}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}Extinction Times}{21}{subsection.4.1.1}
\contentsline {subsection}{\numberline {4.1.2}Persistent System}{22}{subsection.4.1.2}
\contentsline {subsection}{\numberline {4.1.3}Spatial Indices}{22}{subsection.4.1.3}
\contentsline {section}{\numberline {4.2}Multiple Species and Birth and Death Probabilities}{23}{section.4.2}
\contentsline {chapter}{\numberline {5}Results and Analysis}{25}{chapter.5}
\contentsline {section}{\numberline {5.1}Replication of Ruxton and Saravia with added Gillespie Simulator}{25}{section.5.1}
\contentsline {section}{\numberline {5.2}Multiple Species and Birth and Death Probabilities}{28}{section.5.2}
\contentsline {subsection}{\numberline {5.2.1}Species With The Same Birth and Death Probabilities}{29}{subsection.5.2.1}
\contentsline {subsection}{\numberline {5.2.2}Species With Different Birth and Death Probabilities}{32}{subsection.5.2.2}
\contentsline {section}{\numberline {5.3}Analysis of Experiments}{34}{section.5.3}
\contentsline {chapter}{\numberline {6}Conclusion}{38}{chapter.6}
\contentsline {section}{\numberline {6.1}Conclusion of Results}{38}{section.6.1}
\contentsline {subsection}{\numberline {6.1.1}Replication of Ruxton and Saravia with added Gillespie Simulator}{38}{subsection.6.1.1}
\contentsline {subsection}{\numberline {6.1.2}Multiple Species and Birth and Death Probabilities}{38}{subsection.6.1.2}
\contentsline {section}{\numberline {6.2}Future Work}{39}{section.6.2}
\contentsline {section}{\numberline {6.3}Overall Conclusion}{40}{section.6.3}
\contentsline {chapter}{Bibliography}{41}{section.6.3}
\contentsline {chapter}{\numberline {A}User Manual}{42}{appendix.A}
